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97 NOTES CHAPTER I 1 Antonio Favaro, Archimede (Genoa: Formiggini, 1912), 52–53 (translator’s rendering, hic et passim). 2 Reviel Netz, “Archimedes,” in Storia della Scienza, ed. Sandro Petruccioli et al., vol. 1 (Rome: Istituto della Enciclopedia Italiana, 2001), 781. 3 Attilio Frajese, ed., Opere di Archimede, Classici della Scienza (Turin: UTET, 1974), 20. 4 Discussed further in chap. 8. 5 In the planetarium the movements of the sun, the moon and the five then-known planets (Mercury, Venus, Mars, Jupiter, Saturn, i.e., those visible to the naked eye) were imitated exactly. The machine could be used to represent the formation of the eclipse: “And for this reason the invention of Archimedes must be admired because he had figured out how, in the midst of very dissimilar motions, one single rotation could maintain the course of the planets , though they be unequal and various” (Cicero, De re publica 1.21). Arab sources mention a work of Archimedes, On the Construction of the Sphere, in which the scientist seems to have given specific instructions to make the planetarium. 98 NOTES TO PP. 15–24 CHAPTER II 1 The letter π comes from the first letter of the Greek word “periphery ” (i.e., circumference), but its use as a mathematical symbol dates back to the seventeenth century; before that, among the many different symbols employed, one also finds the Latin letter “p” used to express the same concept. 2 1 Kings 7:23. 3 Geoffrey E. R. Lloyd, Greek Science after Aristotle (New York: W. W. Norton, 1973), 44. 4 Gaetano Fichera, “Rigore e profondità nella concezione di Archimede della matematica quantitativa,” in Archimede: Mito, Tradizione , Scienza. Atti del convegno (Siracusa–Catania, 9–12 ottobre 1989), ed. Corrado Dollo (Florence: Olschki, 1992), 4. There is, moreover, no lack of linguistic arguments (e.g., the disappearance of every trace of Doric dialect spoken by Archimedes in his own time) and issues associated with his works’ content (e.g., the second and third theorems are presented in inverse order to how they should be) to sustain the notion that the work that has come to us is not the original but a redaction edited in late antiquity . It has even been suggested that this edition could have been produced by Hypatia, a mathematician and Neoplatonic philosopher who died at the hands of Christians in Alexandria in 415 AD. Such is the hypothesis of Wilbur Richard Knorr in his Textual Studies in Ancient and Medieval Geometry (Boston: Birkhäuser, 1989). 5 Fichera, “Rigore e profondità,” 9. 6 Moreover, the depth and complexity of the work of Archimedes in its historical and scientific reality was able to be understood only upon the discovery of his treatise The Method on Mechanical Theorems at the beginning of the twentieth century (to be discussed further in chap. 8). CHAPTER III 1 An interesting treatment of the argument can be found in an article by the physicist Dionigi Galletto, “La teoria della leva nell’opera di Archimede e la critica ad essa rivolta da Mach,” in Dollo, Archimede , 415–75. Further on Mach’s criticisms, cf. Eduard Jan Dijksterhuis , Archimedes, trans. C. Dikshoorn (Princeton: Princeton University Press, 1987), 291–96. 2 Archimedes’ famous expression “Give me a place to stand and I will move the world” (δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω) is recorded [3.236.111.234] Project MUSE (2024-03-19 04:20 GMT) NOTES TO PP. 26–36 99 by Pappus of Alexandria (a mathematician of the 4C AD), by Simplicius of Cilicia (6C) in his commentary on Aristotelean physics, and by the Byzantine John Tzetzes (12C), who mentions it in the Doric dialect spoken by Archimedes in Syracuse (Various Stories 35, 129–30: this was also called the Chiliads because it was divided into sections of a thousand lines each). 3 For a mathematical description of these, see Dijksterhuis, Archimedes , 405–8. CHAPTER IV 1 See Maria Losito, “La ricostruzione della volute del capitello ionico vitruviano nel Rinascimento italiano,” in the appendix of Vitruvio, De architectura, ed. Pierre Gros, trans. Antonio Corso and Elisa Romano (Turin: Enandi, 1997), 1409–28. 2 Galileo’s enthusiasm for “the marvelous spirals of Archimedes” is evident when in 1638 the Pisan scientist, almost to the letter, reprises the proposition of Archimedes at the beginning of his treatment of uniform motion (de motu aequabili) in his Discourses and Mathematical Demonstrations relating to Two New Sciences (Day I, VIII). 3 Netz, “Archimede,” 789. 4 An interesting version of the episode is found later in Carmen de ponderibus...